A Consensus Based Method for Tracking Modelling Background S(7)

Modelling of the background (“uninteresting parts of the scene”), and of the foreground, play important roles in the tasks of visual detection and tracking of objects. This paper presents an effective and adaptive background modelling method for detectin

approach is more robust (to deviations from the arbitrarily assumed background PDF model), easier to compute, and, as we show experimentally, performs very well.

2.2 Sample Consensus in Background Modelling - SACON

We now define a background model Sample Consensus inspired by the work of RANSAC [7] (which was designed for parametric model fitting).

We keep a cache (or history) of N background samples at each pixel, so that at time t we have {xi(m)|i=1,...,N,N<t} where xt(m) is an observation at pixel m at time t. Note: each observation xt(m)=(xtC1(m),...,xtCk(m)) has k channels (e.g., in RGB color space, each observation is expressed by three channels of R, G, B). For each sample in this cache, we define a binary label capturing the notion of “agreement” between the channel values at the current sample and past channel values at that pixel:

cc 1ifx(m) x it(m)≤Trc Γi(m,t)= 0otherwise (1)

where Tris a threshold value related to the residual ri(m, t)=xic(m) xtc(m) (the choice of Trwill be discussed in section 2.3.4).

The sample consensus is simply formed by counting the number of times previous samples “agree” with the current sample:

Nc 1∑Γ(m,t)≥Tn c∈C1,...Ck Bt(m)= i=1i 0otherwise {} (2)

where Tn is a value thresholding the number of data points that are within the error tolerance Tr of a mode. Bt is a binary value with “one” for a background pixel and “zero” for a foreground pixel. 7